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Stock Valuation
P.V. Viswanath
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P.V. Viswanath 2
Key Concepts and Skills
Understand how stock prices depend on future dividends and dividend growth
Be able to compute stock prices using the dividend growth model
Understand how corporate directors are elected Understand how stock markets work Understand how stock prices are quoted
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P.V. Viswanath 3
Chapter Outline
Common Stock Valuation Some Features of Common and Preferred Stocks The Stock Markets
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P.V. Viswanath 4
Cash Flows to Stockholders
If you buy a share of stock, you can receive cash in two ways The company pays dividends You sell your shares, either to another investor in the
market or back to the company
As with bonds, the price of the stock is the present value of these expected cash flows
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P.V. Viswanath 5
One Period Example
Suppose you are thinking of purchasing the stock of Moore Oil, Inc. and you expect it to pay a $2 dividend in one year and you believe that you can sell the stock for $14 at that time. If you require a return of 20% on investments of this risk, what is the maximum you would be willing to pay?
Compute the PV of the expected cash flows Price = (14 + 2) / (1.2) = $13.33 Or FV = 16; I/Y = 20; N = 1; CPT PV = -13.33
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P.V. Viswanath 6
Two Period Example
Now what if you decide to hold the stock for two years? In addition to the dividend in one year, you expect a dividend of $2.10 in and a stock price of $14.70 at the end of year 2. Now how much would you be willing to pay? PV = 2 / (1.2) + (2.10 + 14.70) / (1.2)2 = 13.33 Or CF0 = 0; C01 = 2; F01 = 1; C02 = 16.80; F02 = 1;
NPV; I = 20; CPT NPV = 13.33
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P.V. Viswanath 7
Three Period Example
Finally, what if you decide to hold the stock for three periods? In addition to the dividends at the end of years 1 and 2, you expect to receive a dividend of $2.205 at the end of year 3 and a stock price of $15.435. Now how much would you be willing to pay?
PV = 2 / 1.2 + 2.10 / (1.2)2 + (2.205 + 15.435) / (1.2)3 = 13.33 Or CF0 = 0; C01 = 2; F01 = 1; C02 = 2.10; F02 = 1; C03 = 17.64;
F03 = 1; NPV; I = 20; CPT NPV = 13.33
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P.V. Viswanath 8
Developing The Model
You could continue to push back when you would sell the stock
You would find that the price of the stock is really just the present value of all expected future dividends
So, how can we estimate all future dividend payments?
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P.V. Viswanath 9
Estimating Dividends: Special Cases
Constant dividend The firm will pay a constant dividend forever This is like preferred stock The price is computed using the perpetuity formula
Constant dividend growth The firm will increase the dividend by a constant percent every
period Supernormal growth
Dividend growth is not consistent initially, but settles down to constant growth eventually
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P.V. Viswanath 10
Zero Growth
If dividends are expected at regular intervals forever, then this is like preferred stock and is valued as a perpetuity
P0 = D / R Suppose stock is expected to pay a $0.50 dividend
every quarter and the required return is 10% with quarterly compounding. What is the price? P0 = .50 / (.1 / 4) = $20
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P.V. Viswanath 11
Dividend Growth Model
Dividends are expected to grow at a constant percent per period. P0 = D1 /(1+R) + D2 /(1+R)2 + D3 /(1+R)3 + …
P0 = D0(1+g)/(1+R) + D0(1+g)2/(1+R)2 + D0(1+g)3/(1+R)3 + …
With a little algebra, this reduces to:
g-R
D
g-R
g)1(DP 10
0
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P.V. Viswanath 12
DGM – Example 1
Suppose Big D, Inc. just paid a dividend of $.50. It is expected to increase its dividend by 2% per year. If the market requires a return of 15% on assets of this risk, how much should the stock be selling for?
P0 = .50(1+.02) / (.15 - .02) = $3.92
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P.V. Viswanath 13
DGM – Example 2
Suppose TB Pirates, Inc. is expected to pay a $2 dividend in one year. If the dividend is expected to grow at 5% per year and the required return is 20%, what is the price? P0 = 2 / (.2 - .05) = $13.33 Why isn’t the $2 in the numerator multiplied by (1.05) in
this example?
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P.V. Viswanath 14
Stock Price Sensitivity to Dividend Growth, g
0
50
100
150
200
250
0 0.05 0.1 0.15 0.2
Growth Rate
Sto
ck P
rice
D1 = $2; R = 20%
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P.V. Viswanath 15
Stock Price Sensitivity to Required Return, R
0
50
100
150
200
250
0 0.05 0.1 0.15 0.2 0.25 0.3
Growth Rate
Sto
ck P
rice
D1 = $2; g = 5%
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P.V. Viswanath 16
Example 7.3 Gordon Growth Company - I
Gordon Growth Company is expected to pay a dividend of $4 next period and dividends are expected to grow at 6% per year. The required return is 16%.
What is the current price? P0 = 4 / (.16 - .06) = $40 Remember that we already have the dividend expected
next year, so we don’t multiply the dividend by 1+g
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P.V. Viswanath 17
Example 7.3 – Gordon Growth Company II
What is the price expected to be in year 4? P4 = D4(1 + g) / (R – g) = D5 / (R – g) P4 = 4(1+.06)4 / (.16 - .06) = 50.50
What is the implied return given the change in price during the four year period? 50.50 = 40(1+return)4; return = 6% PV = -40; FV = 50.50; N = 4; CPT I/Y = 6%
The price grows at the same rate as the dividends
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P.V. Viswanath 18
Nonconstant Growth Problem Statement
Suppose a firm is expected to increase dividends by 20% in one year and by 15% in two years. After that dividends will increase at a rate of 5% per year indefinitely. If the last dividend was $1 and the required return is 20%, what is the price of the stock?
Remember that we have to find the PV of all expected future dividends.
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P.V. Viswanath 19
Nonconstant Growth – Example Solution
Compute the dividends until growth levels off D1 = 1(1.2) = $1.20 D2 = 1.20(1.15) = $1.38 D3 = 1.38(1.05) = $1.449
Find the expected future price P2 = D3 / (R – g) = 1.449 / (.2 - .05) = 9.66
Find the present value of the expected future cash flows
P0 = 1.20 / (1.2) + (1.38 + 9.66) / (1.2)2 = 8.67
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P.V. Viswanath 20
Quick Quiz: Part 1
What is the value of a stock that is expected to pay a constant dividend of $2 per year if the required return is 15%?
What if the company starts increasing dividends by 3% per year, beginning with the next dividend? The required return stays at 15%.
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P.V. Viswanath 21
Using the DGM to Find R
Start with the DGM:
gP
D g
P
g)1(D R
Rfor solve and rearrange
g-R
D
g - R
g)1(DP
0
1
0
0
100
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P.V. Viswanath 22
Finding the Required Return - Example
Suppose a firm’s stock is selling for $10.50. They just paid a $1 dividend and dividends are expected to grow at 5% per year. What is the required return? R = [1(1.05)/10.50] + .05 = 15%
What is the dividend yield? 1(1.05) / 10.50 = 10%
What is the capital gains yield? g =5%
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P.V. Viswanath 23
Features of Common Stock
Voting Rights Proxy voting Classes of stock Other Rights
Share proportionally in declared dividends Share proportionally in remaining assets during
liquidation Preemptive right – first shot at new stock issue to
maintain proportional ownership if desired
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P.V. Viswanath 24
Dividend Characteristics
Dividends are not a liability of the firm until a dividend has been declared by the Board
Consequently, a firm cannot go bankrupt for not declaring dividends
Dividends and Taxes Dividend payments are not considered a business expense,
therefore, they are not tax deductible Dividends received by individuals are taxed as ordinary income Dividends received by corporations have a minimum 70%
exclusion from taxable income
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P.V. Viswanath 25
Features of Preferred Stock
Dividends Stated dividend that must be paid before dividends can be
paid to common stockholders Dividends are not a liability of the firm and preferred
dividends can be deferred indefinitely Most preferred dividends are cumulative – any missed
preferred dividends have to be paid before common dividends can be paid
Preferred stock generally does not carry voting rights
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P.V. Viswanath 26
Stock Market
Dealers vs. Brokers New York Stock Exchange (NYSE)
Members (Specialist system) Operations Floor activity
NASDAQ Not a physical exchange – computer based quotation
system Large portion of technology stocks
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P.V. Viswanath 27
Reading Stock Quotes
Sample Quote
19.2 57.91 42.59 Coca-Cola KO .80 1.4 36 26927 56.20 +0.74
What information is provided in the stock quote?
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P.V. Viswanath 28
Quick Quiz: Part 2
You observe a stock price of $18.75. You expect a dividend growth rate of 5% and the most recent dividend was $1.50. What is the required return?
What are some of the major characteristics of common stock?
What are some of the major characteristics of preferred stock?